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The implementation of star formation and stellar feedback in cosmologicalsimulations plays a critical role in shaping galaxy properties. In the firstpaper of the series, we presented a new method to model star formation as acollection of star clusters. In this paper, we improve the algorithm byeliminating accretion gaps, boosting momentum feedback, and introducing asubgrid initial bound fraction, $f_i$, that distinguishes cluster mass fromstellar particle mass. We perform a suite of simulations with different starformation efficiency per freefall time $\epsilon_{\rm ff}$ and supernovamomentum feedback intensity $f_{\rm boost}$. We find that the star formationhistory of a Milky Way-sized galaxy is sensitive to $f_{\rm boost}$, whichallows us to constrain its value, $f_{\rm boost}\approx5$, in the currentsimulation setup. Changing $\epsilon_{\rm ff}$ from a few percent to 200\% haslittle effect on global galaxy properties. However, on smaller scales, theproperties of star clusters are very sensitive to $\epsilon_{\rm ff}$. We findthat $f_i$ increases with $\epsilon_{\rm ff}$ and cluster mass. Through thedependence on $f_i$, the shape of the cluster initial mass function variesstrongly with $\epsilon_{\rm ff}$. The fraction of clustered star formation andmaximum cluster mass increase with the star formation rate surface density,with the normalization of both relations dependent on $\epsilon_{\rm ff}$. Thecluster formation timescale systematically decreases with increasing$\epsilon_{\rm ff}$. Local variations in the gas accretion history lead to a0.25~dex scatter for the integral cluster formation efficiency. Jointconstraints from all the observables prefer the runs that produce a medianintegral efficiency of 16\%.

Star Cluster Formation in Cosmological Simulations. II. Effects of Star Formation Efficiency and Stellar Feedback